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On the topological Hochschild homology of Johnson-Wilson spectra

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HHHW03 - Derived algebraic geometry and chromatic homotopy theory

Let E(n) denote the n-th Johnson-Wilson spectrum at an odd prime p. The spectrum E(1) coincides with the Adams summand of p-local topological K-theory. McClure and Staffeldt offered an intriguing computation of THH ), showing that it splits as a wedge sum of E(1) and a rationalized suspension of E(1).   In joint work with Birgit Richter, we study the Morava K-theories of THH ), with an aim at investigating if McClure-Staffeldt's splitting in lower chromatic pieces generalizes.  Under the assumption that E(2) is commutative, we show that THH ) splits as a wedge sum of E(2) and its lower chromatic localizations.

This talk is part of the Isaac Newton Institute Seminar Series series.

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